Black hole physics

For a long time, I'm having difficulties understanding some problems of black hole physics, so maybe someone here could help me out. Standard story goes something like this : while a massive star's undergoes gravitational collapse, it's core goes through phase transition (p+e -> n +v) transforming itself into neutron star. Let's say it's mass is over x solar masses, than collapse will go on until it reaches state of a black hole. Nothing can exit it, it has singularity point of a infinite spacetime curvation where laws of physics can't be defined.

Basically, existence of singularity is what I don't understand.

Let's say I'm *really* good in calculus and I take a well-localized mass distribution of total 10 (or whatever ) solar masses of 'ideal fluid'. I throw it in field equation and I receive black hole metrics in limit of t -> oo , measured by a distant observer, right?

Ok, now let's go a bit back in time , to phase transition between radiation dominated and matter dominated era after the Big Bang. If we plug in different equations-of-state of radiation and matter in Friedmann equations, we will get different dynamics of metrics e.g. time dependence of a scale-of-space changes. (term is translated from croatian, maybe not correct)

Now, in Big Bang physics it is obvious that a dynamics of such system *will* depend on equation of state of it's mass distribution that contribute to energy density. How come black hole's doesn't ? Late Big Bang physics, as I see it, is all about introducing detailed equation of state into Einstein's field equations to reproduce visible consequences in t ~ 10^10 years.

OTOH, for some unknown (maybe only to me) reason, it's reasonable to approximate core of a collapsing star with a ideal fluid of a quite impotent equation of state that gives a singular "core" instead of a quark-gluon-graviton plasma enclosed with a Schwarzschild surface=) I'm kidding about the "plasma", but I hope you get the point. I am not challenging validity of a Schwarzschild solution to *some* extent and I understand that system of a coupled, nonlinear , partial differential equation are hard to solve so approximations are a life-style. But then, physicist are cautious when talking about consequences of a models that incorporate such *strong* assumptions, except when they talk about BH singularities as if they are experimental fact and not remnant of a wild assumption that disregards all others forces of nature except gravity! So...what am I missing?

remnant of a wild assumption that disregards all others forces of nature except gravity! So...what am I missing?

There is one important point you are missing: Every force you imagine to stop the collapse will do so by adding pressure, which balances the gravitational pull. And pressure gravitates, that means, the more pressure to balance gravtiy, the more gravity to be balanced. Collapse is inevitable.

There is one important point you are missing: Every force you imagine to stop the collapse will do so by adding pressure, which balances the gravitational pull. And pressure gravitates, that means, the more pressure to balance gravtiy, the more gravity to be balanced. Collapse is inevitable.

Indeed. As purly mathematical objection, I could insist on a EOS that has negative pressure pole at finite density - collapse would not be inevitable.

Second , to my mind, there should be critical limit that discriminates systems that have pressure big enough to balance gravity, but small enough not to contribute to energy density much - having stabile future ( like white dwarfs ?) and OTOH systems that any additional pressure rises gravity pressure due to rise of energy density and are unstabile (e.g. black hole) My question then would be : how do we know that neutron gas ( or any OTHER phase that neutron gas might transform into ) is over such limit since supernuclear densities is way out of our experimental reach?

Does anyone know any book titles that talk on these problems on undergraduate level, btw?